Model Results

June 24, 2019

I. Summary statistics and trace plots


## 
## Iterations = 105010:120000
## Thinning interval = 10 
## Number of chains = 3 
## Sample size per chain = 1500 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##                         Mean      SD Naive SE Time-series SE
## alpha.p[1]           2.91715 0.15168 0.002261       0.002261
## alpha.p[2]           3.00976 0.17129 0.002553       0.003065
## alpha.p[3]           1.82537 0.09324 0.001390       0.001390
## beta.repro.gamma[1]  1.24844 0.37153 0.005538       0.009039
## beta.repro.gamma[2]  2.09554 0.41723 0.006220       0.012672
## beta.repro.gamma[3]  0.78915 0.43977 0.006556       0.007498
## beta.repro.gamma[4]  0.39880 0.38402 0.005725       0.007707
## beta.repro.phi[1]    1.67960 0.40987 0.006110       0.010687
## beta.repro.phi[2]    0.94146 0.32070 0.004781       0.006889
## beta.repro.phi[3]    0.03826 0.49545 0.007386       0.009994
## beta.repro.phi[4]    0.55898 0.30671 0.004572       0.005487
## beta.rgr.gamma[1]   -0.21580 0.12976 0.001934       0.002281
## beta.rgr.gamma[2]    0.09966 0.12385 0.001846       0.002984
## beta.rgr.phi[1]      0.02314 0.17124 0.002553       0.003702
## beta.rgr.phi[2]     -0.12046 0.10787 0.001608       0.001638
## beta.d.gamma[1]      0.60192 0.15362 0.002290       0.002440
## beta.d.gamma[2]      5.48693 1.03769 0.015469       0.101622
## beta.d.p[1]          0.89585 0.24346 0.003629       0.003658
## beta.d.p[2]          0.96074 0.30539 0.004552       0.005481
## beta.d.p[3]          0.44147 0.09487 0.001414       0.001465
## beta.d.phi[1]        0.23406 0.11098 0.001654       0.001687
## beta.d.phi[2]        0.75160 0.29840 0.004448       0.005120
## beta.d.psi[1]        1.34199 0.18900 0.002817       0.003320
## beta.d.psi[2]        1.75418 0.20977 0.003127       0.004558
## mu.gamma[1]         -2.32775 0.34190 0.005097       0.009462
## mu.gamma[2]         -3.02206 0.41084 0.006125       0.013849
## mu.gamma[3]          3.61873 0.77205 0.011509       0.066458
## mu.gamma[4]          3.59564 0.72827 0.010856       0.065766
## mu.phi[1]           -0.35789 0.38012 0.005666       0.011868
## mu.phi[2]            0.22133 0.30210 0.004504       0.008098
## mu.phi[3]            1.95298 0.41526 0.006190       0.011071
## mu.phi[4]            1.57203 0.23931 0.003567       0.005524
## mu.psi[1]           -0.16899 0.20725 0.003089       0.003349
## mu.psi[2]            0.25089 0.19389 0.002890       0.003123
## mu.psi[3]            1.50218 0.23363 0.003483       0.005159
## mu.psi[4]            1.40405 0.16919 0.002522       0.004386
## sigma.gamma          0.98639 0.15687 0.002338       0.005689
## sigma.phi            0.92391 0.17669 0.002634       0.007452
## sigma.psi[1]         1.08785 0.20299 0.003026       0.005519
## sigma.psi[2]         0.73828 0.19920 0.002969       0.008740
## 
## 2. Quantiles for each variable:
## 
##                         2.5%      25%      50%      75%    97.5%
## alpha.p[1]           2.62667  2.80881  2.91650  3.01852  3.22703
## alpha.p[2]           2.69529  2.88956  3.00617  3.12138  3.35906
## alpha.p[3]           1.64449  1.76263  1.82513  1.88840  2.00587
## beta.repro.gamma[1]  0.53413  0.99615  1.24145  1.49872  1.98888
## beta.repro.gamma[2]  1.32163  1.80119  2.08052  2.37140  2.95731
## beta.repro.gamma[3] -0.03415  0.48717  0.77958  1.07635  1.69064
## beta.repro.gamma[4] -0.33965  0.13761  0.39778  0.66228  1.14629
## beta.repro.phi[1]    0.90613  1.40448  1.67091  1.95607  2.49460
## beta.repro.phi[2]    0.32602  0.73147  0.93723  1.14811  1.59328
## beta.repro.phi[3]   -0.92263 -0.29393  0.04660  0.37585  1.01055
## beta.repro.phi[4]   -0.03689  0.35073  0.55900  0.76851  1.16716
## beta.rgr.gamma[1]   -0.47650 -0.30324 -0.21335 -0.12870  0.03164
## beta.rgr.gamma[2]   -0.13348  0.01657  0.09727  0.18092  0.35344
## beta.rgr.phi[1]     -0.30804 -0.08904  0.01992  0.13765  0.35840
## beta.rgr.phi[2]     -0.32802 -0.19452 -0.12223 -0.05096  0.10276
## beta.d.gamma[1]      0.31172  0.49882  0.60135  0.70205  0.90360
## beta.d.gamma[2]      3.74607  4.70500  5.39357  6.16768  7.70185
## beta.d.p[1]          0.44064  0.72333  0.89198  1.06000  1.38579
## beta.d.p[2]          0.39707  0.74820  0.95167  1.16226  1.59031
## beta.d.p[3]          0.26286  0.37655  0.44060  0.50261  0.63314
## beta.d.phi[1]        0.02384  0.15764  0.23425  0.30700  0.45566
## beta.d.phi[2]        0.19752  0.54665  0.74107  0.94446  1.36071
## beta.d.psi[1]        0.98811  1.21055  1.33494  1.46481  1.73056
## beta.d.psi[2]        1.36394  1.60671  1.75231  1.89176  2.17581
## mu.gamma[1]         -3.03859 -2.55048 -2.31626 -2.09438 -1.70433
## mu.gamma[2]         -3.89526 -3.28014 -3.00122 -2.73481 -2.27199
## mu.gamma[3]          2.26178  3.04180  3.56447  4.13581  5.16608
## mu.gamma[4]          2.36735  3.04246  3.53996  4.07209  5.14876
## mu.phi[1]           -1.11715 -0.60858 -0.35894 -0.10603  0.39451
## mu.phi[2]           -0.37957  0.01675  0.22358  0.42387  0.81019
## mu.phi[3]            1.18547  1.66482  1.93290  2.20831  2.81974
## mu.phi[4]            1.12471  1.40592  1.56303  1.73149  2.05410
## mu.psi[1]           -0.58748 -0.30446 -0.16883 -0.03087  0.23223
## mu.psi[2]           -0.13088  0.12514  0.25010  0.37993  0.63287
## mu.psi[3]            1.07171  1.34170  1.49130  1.65350  1.99132
## mu.psi[4]            1.09034  1.29185  1.39575  1.51214  1.76066
## sigma.gamma          0.70094  0.87679  0.97697  1.08589  1.32029
## sigma.phi            0.58651  0.80190  0.91903  1.03918  1.28802
## sigma.psi[1]         0.70994  0.95087  1.08278  1.21974  1.51472
## sigma.psi[2]         0.37503  0.59868  0.73175  0.86904  1.14977


II. Gelman-Rubin diagnostic


## Potential scale reduction factors:
## 
##                     Point est. Upper C.I.
## alpha.p[1]                1.00       1.00
## alpha.p[2]                1.00       1.00
## alpha.p[3]                1.00       1.00
## beta.repro.gamma[1]       1.00       1.01
## beta.repro.gamma[2]       1.00       1.00
## beta.repro.gamma[3]       1.00       1.00
## beta.repro.gamma[4]       1.00       1.01
## beta.repro.phi[1]         1.00       1.00
## beta.repro.phi[2]         1.00       1.00
## beta.repro.phi[3]         1.00       1.00
## beta.repro.phi[4]         1.00       1.00
## beta.rgr.gamma[1]         1.00       1.00
## beta.rgr.gamma[2]         1.00       1.01
## beta.rgr.phi[1]           1.00       1.00
## beta.rgr.phi[2]           1.00       1.00
## beta.d.gamma[1]           1.00       1.00
## beta.d.gamma[2]           1.02       1.06
## beta.d.p[1]               1.00       1.00
## beta.d.p[2]               1.00       1.00
## beta.d.p[3]               1.00       1.00
## beta.d.phi[1]             1.00       1.00
## beta.d.phi[2]             1.00       1.00
## beta.d.psi[1]             1.00       1.00
## beta.d.psi[2]             1.00       1.01
## mu.gamma[1]               1.00       1.01
## mu.gamma[2]               1.00       1.00
## mu.gamma[3]               1.02       1.06
## mu.gamma[4]               1.02       1.07
## mu.phi[1]                 1.00       1.00
## mu.phi[2]                 1.00       1.00
## mu.phi[3]                 1.00       1.00
## mu.phi[4]                 1.00       1.01
## mu.psi[1]                 1.00       1.00
## mu.psi[2]                 1.00       1.01
## mu.psi[3]                 1.00       1.00
## mu.psi[4]                 1.00       1.01
## sigma.gamma               1.00       1.01
## sigma.phi                 1.00       1.01
## sigma.psi[1]              1.00       1.01
## sigma.psi[2]              1.02       1.06
## 
## Multivariate psrf
## 
## 1.03


III. Posterior predictive check


Scatterplot of summed squared residuals. The Bayesian posterior predictive check p-value was 0.37.